Operational Research Pdf

Operations Research Online Quiz Following quiz provides Multiple Choice Questions (MCQs) related to OS. You will have to read all the given answers and click on view answer option.

IEOR 4004: Introduction to Operations Research - Deterministic Models. The notes were meant to provide a succint summary of the material, most of which was loosely based on the book Winston-Venkataramanan: Introduction to Mathematical Programming (4th ed.), Brooks/Cole 2003. Other material (such as the dictionary notation) was adapted. “Operation research is a scientific method of providing executive departments with a quantities basis for decisions regarding the operations under their control”. “Operation research is concerned with scientifically deciding how best to design and operate man machine systems usually under conditions requiring the allocation of & care resources”. 1 Full PDF related to this paper. QUESTION BANK ON OPERATIONS RESEARCH UNIT-1: Basics of operations research. QUESTION BANK ON OPERATIONS RESEARCH UNIT-1: Basics of operations research. Explain the meaning of linear programming problem stating its uses and give its limitations.Q5. Write at least five.

These HTML online test quizzes on Operations Research have answers available with pdf, which is very useful in interview and also in HTML subject exam.

Question 1: Operations Research approach is?

(A) multi-disciplinary

(B) scientific

(C) intuitive

(D) collect essential data

(A) multi-disciplinary

Question 2: Operation research approach is typically based on the use of ___________.

(A) physical model

(B) mathematical model

(C) iconic model

(D) descriptive model

(B) mathematical model

Question 3: Mathematical model of linear programming problem is important because ___________.

(A) it helps in converting the verbal description and numerical data into mathematical expression

(B) decision makers prefer to work with formal models

(C) it captures the relevant relationship among decision factors

(D) it enables the use of algebraic technique

(A) it helps in converting the verbal description and numerical data into mathematical expression

Question 4: In Program Evaluation Review Technique for an activity, the optimistic time 2, the pessimistic time is 12 and most-likely time is 4. What is the expected time?

(A) 0

(B) 1

(C) 5

(D) 6

(C) 5

Question 5: Graphical method of linear programming is useful when the number of decision variable are __________.

(A) 2

(B) 2

(C) finite

(D) infinite

(A) 2

Question 6: A feasible solution to a linear programming problem _______________.

(A) must satisfy all the constraints of the problem simultaneously

(B) need not satisfy all of the constraints, only some of them

(C) must be a corner point of the feasible region.

(D) must optimize the value of the objective function

(A) must satisfy all the constraints of the problem simultaneously

Question 7: Utilization factor is also known as ___________.

(A) Traffic intensity

(B) Kendals notation

(C) Row minima method

(D) Unbalanced assignment problem

(A) Traffic intensity

Question 8: While solving a linear programming problem in feasibility may be removed by _________.

(A) adding another constraint

(B) adding another variable

(C) removing a constraint

(D) removing a variable

(C) removing a constraint

Question 9: In the optimal simplex table, Zj-Cj=0 value indicates _____________.

(A) alternative solution

(B) bounded solution

(C) infeasible solution

(D) unbounded solution

(A) alternative solution

Question 10: If all aij values in the entering variable column of the simplex table are negative, then ___________.

(A) there are multiple solutions

(B) there exist no solution

(C) solution is degenerate

(D) solution is unbounded

(D) solution is unbounded

/how-to-hack-someones-clash-of-clans-id/. Question 11: If an artificial variable is present in the basic variable column of optimal simplex table, then the solution is ___________.

(A) alternative

(B) bounded

(C) no solution

(D) infeasible

(D) infeasible

Question 12: For any primal problem and its dual ______________.

(A) optimal value of objective function is same

(B) primal will have an optimal solution iff dual does too

(C) both primal and dual cannot be infeasible

(D) dual will have an optimal solution iff primal does too

(B) primal will have an optimal solution iff dual does too

Question 13: Principle of complementary slackness states that ____________.

(A) primal slack*dual main=0

(B) primal main+dual slack=0

(C) primal main+dual surplus=0

(D) dual slack*primal main not equal to zero

(A) primal slack*dual main=0

Question 14: If primal linear programming problem has a finite solution, then dual linear programming problem should have ____________.

(A) finite solution

Operational Research Pdf

(B) infinite solution

(C) bounded solution

(D) alternative solution


Question 15: The initial solution of a transportation problem can be obtained by applying any known method. How-ever, the only condition is that __________.

(A) the solution be optimal

(B) the rim conditions are satisfied

(C) the solution not be degenerate

(D) the few allocations become negative

(B) the rim conditions are satisfied

Question 16: The dummy source or destination in a transportation problem is added to ______________.

(A) satisfy rim conditions

(B) prevent solution from becoming degenerate

(C) ensure that total cost does not exceed a limit

(D) the solution not be degenerate

(A) satisfy rim conditions

Question 17: Which of the following methods is used to verify the optimality of the current solution of the transportation problem ____________.

(A) Modified Distribution Method

(B) Least Cost Method

(C) Vogels Approximation Method

(D) North West Corner Rule

(A) Modified Distribution Method

Question 18: An optimal assignment requires that the maximum number of lines which can be drawn through squares with zero opportunity cost be equal to the number of ________.

(A) rows or coloumns

(B) rows and coloumns

(C) rows+columns- 1

(D) rows-columns

(A) rows or coloumns

Question 19: Maximization assignment problem is transformed into a minimization problem by _____________.

(A) adding each entry in a column from the maximum value in that column X plane 11 crack torrent.

(B) subtracting each entry in a column from the maximum value in that column

(C) subtracting each entry in the table from the maximum value in that table

(D) adding each entry in the table from the maximum value in that table

(C) subtracting each entry in the table from the maximum value in that table

Question 20: To proceed with the MODI algorithm for solving an assignment problem, the number of dummy allocations need to be added are ___________.

(A) n

(B) n-1

(C) 2n-1

(D) n-2

(B) n-1

Question 21: An artificial variable leaves the basis means, there is no chance for the ________ variable to enter once again.

(A) slack

(B) surplus

(C) artificial

(D) dual

(C) artificial

Question 22: Simplex method was designed by ___________.

(A) Dantzig

(B) A.Charnes

(C) Lemke

(D) Hungarian

(A) Dantzig

Question 23: Dual Simplex Method was introduced by ____________.

(A) Dantzig

(B) A.Charnes

(C) Lemke

(D) Hungarian

(C) Lemke

Question 24: 4. The cell with allocation can be called ___________ .

Operations Research Pdf Notes

(A) Cell

(B) Empty cell

(C) Basic cell

(D) Non-basic cell

(C) Basic cell

Question 25: The cell without allocation is called __________.

(A) Basic cell

(B) Non-basic cell

(C) Empty cell

(D) Basic solution

(B) Non-basic cell

Question 26: Service mechanism in a queuing system is characterized by _____________.

(A) customers behavior

(B) servers behavior

(C) customers in the system

(D) server in the system

(B) servers behavior

Question 27: . The problem of replacement is felt when job performing units fail _______________.

(A) suddenly and gradually

(B) gradually

(C) suddenly

(D) neither gradually nor suddenly

(A) suddenly and gradually

Question 28: Least Cost Method is also known as __________.

(A) North West Corner Method

(B) Matrix Minima Method

(C) Row Minima method

(D) Coloumn Minima method

(B) Matrix Minima Method

Question 29: The objective of network analysis is to ___________.

(A) minimize total project duration

(B) minimize toal project cost

(C) minimize production delays, interruption and conflicts

(D) maximize total project duration

(A) minimize total project duration

Question 30: A activity in a network diagram is said to be __________ if the delay in its start will further delay the project completion time.

(A) forward pass

(B) backward pass

(C) critical

(D) non critical

(C) critical

After reading this article you will learn about:- 1. Definition of Operation Research 2. Applications of Operation Research 3. Methodology 4. Tools.

Definition of Operation Research:

Uniform and acceptable definition of O.R. is not available.

However, few definitions available in literature are given below:


1. “Operation research is a scientific method of providing executive departments with a quantities basis for decisions regarding the operations under their control”.

2. “Operation research is concerned with scientifically deciding how best to design and operate man machine systems usually under conditions requiring the allocation of & care resources”. O.R. Society of America

3. “Operation research is a scientific approach to problem solving for executive management”. H.M. Warner

4. “O.R is the application of scientific method by interdisciplinary teams to problems involving the control of organized (men-machines) systems so as to provide solution which best serve the purpose of the organisation as a whole”.

5. “Operation research is an aid for the executive in making his decisions by providing him with the needed quantitative information based on the scientific method of analysis”.

6. “O.R in the most general sense can be characterized as the application of scientific methods techniques and tools to problems involving the operations of systems so as provide those in control of the operation with optimum solution to the problems”.

Applications of Operation Research:

O.R. is a problem solving and decision taking technique. It is considered a kit of scientific and programmable rules which provides the management a “quantitative basis” for decisions concerning the operation under its control.

Some areas of management where O.R techniques have been successfully utilized are as follow:

1. Allocation and Distribution in Projects:


(i) Optimal allocation of resources such as men materials machines, time and money to projects.

(ii) Determination and deployment of proper workforce.

(iii) Project scheduling, monitoring and control.

2. Production and Facilities Planning:

(i) Factory size and location decision.

(ii) Estimation of number of facilities required.

(iii) Preparation of forecasts for the various inventory items and computation of economic order quantities and reorder levels.

(iv) Scheduling and sequencing of production runs by proper allocation of machines.

(v) Transportation loading and unloading,


(vi) Warehouse location decision.

(vii) Maintenance policy decisions.

3. Programmes Decisions:

(i) What, when and how to purchase to minimize procurement cost.

(ii) Bidding and replacement policies.

4. Marketing:

(i) Advertising budget allocation.

(ii) Product introduction timing.

(iii) Selection of advertising media.

(iv) Selection of product mix.


(v) Customer’s preference of size, colour and packaging of various products.

5. Organization Behaviour:

(i) Selection of personnel, determination of retirement age and skills.

(ii) Recruitment policies and assignment of jobs.

(iii) Recruitment of employees.

(iv) Scheduling of training programs.

6. Finance:

(i) Capital requirements, cash flow analysis.

(ii) Credit policies, credit risks etc.

(iii) Investment decision.

(iv) Profit plan for the company.

7. Research and Development:

(i) Product introduction planning.

(ii) Control of R&D projects.

(iii) Determination of areas for research and development.


(iv) Selection of projects and preparation of their budgets.

(v) Reliability and control of development projects thus it may be concluded that operation research can be widely utilized in management decisions and can also be used as corrective measure.

Methodology of Operation Research:

Quantitative basis for decision making is provided to managers by O.R. it enhances a manager’s ability to make long range plans and to solve the routine problems of running a enterprise/concern OR is a systematic and logical approach to provide a rational footing for taking decisions. Operation research, like scientific research is based on scientific methodology which involves following steps.

1. Formulating the Problem:

OR is a research into the operation of a man machine organisation and must consider the economics of the operation in formulating a problem for O.R. study analysis must be made of the following major components:

(i) The environment.

(ii) The objectives.

(iii) The decision maker.

(iv) The alternative courses of action and constraints out of the above four component, environment is most comprehensive as it provides a setting for the remaining three. The operation researcher shall attend conferences, pay visits, send observation and perform research work thus succeeds in getting sufficient date to formulate the problems.

2. Constructing a Model to Represent the System under Study:

Once the project is approved by the management, the next step is to construct a model for the system under study. The operation researcher can now construct the model to show the relations and interrelations between a cause and effect or between an action and a reaction.

Now the aim of operation researcher is to develop a model which enables him to forecast the effect of factors crucial to the solution of given problem. The proposed model may be tested and modified in order to work under stated environmental constraints. A model may also be modified if the management is not satisfied by its performance.

3. Deriving Solution from the Model:

A solution may be extracted from a model either by conducting experiments on it i.e., by simulation or by mathematical analysis. No model will work appropriately if the data is not appropriate. Such information may be available from the results of experiments or from hunches based on experience.

The data collection can clearly effect the models output significantly. Operation researcher should not assume that once he has defined his objective and model, he has achieved his aim of solving the problem. The required data collection consumes time to prepare if date collection errors are to be minimized

4. Testing the Model and the Solution Derived from it:


As has been pointed out earlier a model is never a perfect representation of reality. But if properly formulated and correctly manipulated, it may be useful in providing/predicting the effect of changes in control variables on overall system effectiveness.

The usefulness or utility of a model is checked by finding out how well it predicts the effect of these changes. Such an analyse is usually known as sensitivity analysis. The utility or validity of the solution can be verified by comparing the results obtained without applying the solution with the results obtained when it is used.

5. Establishing Controls over the Solution:

The next phase for the operation researcher is to explain his findings to the management. It may be pointed out that he should specify those conditions under which the solution can be utilized.

He should also point out weaknesses if any so that management will know what risks they are taking while employing the model to generate results. Thus he should also specify the limits with in which the results obtained from using the model are valid. He should also define those conditions under which the model will not work.

6. Implementation of the Solution:

The last phase of the operation research methodology is implementation of solutions obtained in the previous steps. In operation research though decision making is scientific but its implementation involves so many behavioural issues. Therefore the implementing authority has to resolve the behavioural issues. He has to sell the idea of utility of O.R not only to the workers but also to superiors.

The distance between O.R scientist and management may create huddles thus the gap between one who provides a solution and the other who wants to utilize it must be eliminated. To achieve this both the management and O.R scientist should play positive role A properly implemented solution obtained through application of O.R techniques results in improved working conditions and gains the management support.

Tools of Operation Research:

In any area of human endeavour, whether it is a production system, business system or service system where an objective is to be optimized, the problem falls into the domain of operation research.

Some of the commonly used techniques of operation research are as follows:

1. Linear programming.

2. Waiting line theory or queuing theory.

3. Inventory control models.

4. Replacement problems.

5. Network Analysis.

6. Sequencing.

7. Dynamic programming.

8. Assignment problems.

Operations Research Pdf Free Download

9. Decision theory.

10. Integer Programming.

11. Transportation Problems.

12. Simulation.

13. Goal Programming.

History Of Operational Research Pdf

14. Markov Analysis.

15. Game Theory.

16. Heuristic Models.

17. Routing Models.

18. Symbolic logic.

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